Mathematical Sciences: Residual Intersections and Linkage ofCohen-Macaulay Ideals

这项研究属于交换代数的一般领域。该项目涉及在剩余交下保留哪些环论性质的问题。此外，首席研究者将找到理想处于完全兴趣的连锁类的充要条件。交换环的研究目标之一是对具有某些性质的理想进行分类。这些结果中的许多都应用于代数几何中的问题和对应问题。一个有趣的话题是，一个通过与另一个理想联系在一起的理想是否共享第二个理想的有趣特性，或者它在多大程度上这样做。后一个问题是这个项目的主要关注点。

This research is in the general area of commutative algebra. The project is concerned with the question of which ring theoretic properties are preserved under residual intersections. In addition, the principal investigator will find necessary and sufficient conditions for an ideal to be in the linkage class of a complete interesection. One goal in the study of commutative rings is to classify ideals having certain properties. Many of these results have applications to problems and counterparts in algebraic geometry. One interesting topic is whether an ideal related by linkage to another ideal shares any of the second ideals interesting properties, or to what extent it does so. This latter problem is the primary concern of this project.